Problem Solving

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A. 1/(r+2)
B. 1/(2r+2)
C. 1/(3r+2)
D. 1/(r+3)
E. 1/(2r+3)

Let Henry's income be $100.
Let Henry save $y
So Henry spends $(100 - y)

Next year, as stated- for every $1 Henry saves, he would have $(1 + r) available to spend.
So as he has $y saved this year, he would have $ y*(1+r) available to spend next year.

Now as stated,

next year the amount available to spend will be equal to half the amount that he spends this year

Thus, Amout available to spend next year = 0.5 * amt spent this year
=> y(1+r) = 0.5*(100-y)

Calculate for y
=> y = 100/(3+2r)

Required fraction is:
$Saved/$Earned
=> y/100
=> (100/(3+2r))/100
=> 1/(3+2r)
=> Option E